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Is that based on what you see when you look it up?
cryp·tog·ra·phy
noun
the art of writing or solving codes.
That's a terrible definition, but "codes" is doing the heavy lifting.
It is not a code, in that definition, if it does not require knowledge of a key to decode.
It is literally impossible for anything that doesn't have a secret key to qualify as cryptography. That is the entire defining trait.
no. replacement cyphers are cryptography, too.
The "key" is the mapping of cipher alphabet to message alphabet.
There has to be a secret to be cryptography. The meaning has to be hidden without the secret information (though primitive/weak attempts can have a small enough search space to be brute forced). But the content being hidden without that information is the entirety of what the word means.